This paper proposes a new way to measure the leverage effect and its propagation over time. We also show that, with respect to the newly proposed measure, common volatility models like the GJRGARCH, the Exponential GARCH, and the asymmetric SV can be inaccurate to correctly represent the leverage effect and its propagation for financial time series. We propose to modify the variance recursion of common volatility models by including an auxiliary leverage process which allows for a proper representation of the leverage effect and its propagation over time. Empirical results indicate that the inclusion of the auxiliary leverage process improves both in sample and out of sample.